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A240742 Number of compositions of n having exactly seven fixed points.

%I A240742 #10 Nov 06 2014 09:52:33
%S A240742 1,1,3,7,16,35,76,162,334,706,1457,2996,6130,12496,25383,51423,103937,
%T A240742 209723,422418,849843,1707917,3429407,6881120,13798903,27657921,
%U A240742 55414350,110989891,222243203,444916908,890536103,1782217460,3566301121,7135641348,14276228900
%N A240742 Number of compositions of n having exactly seven fixed points.
%H A240742 Joerg Arndt and Alois P. Heinz, <a href="/A240742/b240742.txt">Table of n, a(n) for n = 28..1000</a>
%F A240742 a(n) ~ c * 2^n, where c = 0.00000000620059990498579334409439332104298331660404026106645127910814204326... . - _Vaclav Kotesovec_, Sep 07 2014
%p A240742 b:= proc(n, i) option remember; `if`(n=0, 1, series(
%p A240742       add(b(n-j, i+1)*`if`(i=j, x, 1), j=1..n), x, 8))
%p A240742     end:
%p A240742 a:= n-> coeff(b(n, 1), x, 7):
%p A240742 seq(a(n), n=28..65);
%t A240742 b[n_, i_] := b[n, i] = If[n == 0, 1, Series[Sum[b[n - j, i + 1]*If[i == j, x, 1], {j, 1, n}], {x, 0, 8}]]; a[n_] := SeriesCoefficient[b[n, 1], {x, 0, 7}]; Table[a[n], {n, 28, 65}] (* _Jean-François Alcover_, Nov 06 2014, after Maple *)
%Y A240742 Column k=7 of A238349 and of A238350.
%K A240742 nonn
%O A240742 28,3
%A A240742 _Joerg Arndt_ and _Alois P. Heinz_, Apr 11 2014